A matheuristic for the stochastic facility location problem

Abstract

In this paper, we describe a matheuristic to solve the stochastic facility location problem which determines the location and size of storage facilities, the quantities of various types of supplies stored in each facility, and the assignment of demand locations to the open facilities, which minimize unmet demand and response time in lexicographic order. We assume uncertainties about demands, inventory spoilage, and transportation network availability. A good example where such a formulation makes sense is the the problem of pre-positioning emergency supplies, which aims to increase disaster preparedness by making the relief items readily available to people in need. The matheuristic employs iterated local search techniques to look for good location and inventory configurations, and uses CPLEX to optimize the assignments. Numerical experiments on a number of case studies and random instances for the pre-positioning problem demonstrate the effectiveness and efficiency of the matheuristic, which is shown to be particularly useful for tackling larger instances that are intractable for exact solvers. The matheuristic is therefore a contribution to the literature on heuristic approaches to solving facility location under uncertainties, can be used to further study the particular variant of the facility location problem, and can also support humanitarian logisticians in their planning of pre-positioning strategies.